Math 2
1
By: Claudia
Subtracting integers:
2 – (-8)
Rule
When we subtract we ADD THE OPPISITE!
(never change the first number!)
2 + 8 is the same as
2 – (-8)…..
So, the answer is the same, 10 
-8 + 2 = -6
The answer is positive because you always use the
sign of the number with the highest absolute
value. -8 is farther away from zero then 2 is. So 8 has the highest absolute value.
Vocab:
Integers – the set of
whole numbers and
their opposites.
Absolute Value – the
distance the number
is from zero on the
number line.
2
How to Multiply Integers
When multiplying integers with the same sign the product is always
positive.
When multiplying integers with different signs the answer will
always be negative.
If any of the integers is zero the result is always zero.
3
Adding Integers
Subtracting
Integers
Ex: 5+3=8 Add the numbers as if they were positive,
 then
Ex: -5-(-3)
add the sign of the numbers.
=-5+3
When
we subtract,
wesign=
ADD THE
1. Adding
Integers
having
the same
OPPOSITE
-5+(-3)=
-8
Ex:
2-1two
then
turns into
2+(-1)
It helps us to get the right
2.Rule:
Adding
integers
having
signs:
answer, too, and less confusing.
Ex: -5+3 Take the difference of the numbers as if they
were positive, then add the sign of the number having
absolute value.
Ex: -5+3=-2
4

Dividing Integers


Multiplying Integers



If a pair of integers has the same sign, then the answer will
have a positive sign. You must calculate the absolute value
of each integer and then divide the first integer by the
second integer.





Step 1: |-10| / |-2| = 10 / 2
Step 2: 10 / 2 = 5
Step 3: Since integers have same sign, answer is
positive: +5


When having two integers with different signs, the product is
always negative



Example 1: -2 · 5 = (-2)+(-2)+(-2)+(-2)+(-2) = -10
Example 2: 2 · (-5) = (-5)+(-5) = -10

When multiplying more than two integers


Example 1: (-1) · (-2) · (-3) = ?

Example: -10 / +2 = ?

Step 1: |-10| / |+2| = 10 / 2
Step 2: 10 / 2 = 5
Step 3: Since integers have different signs,
negative: -5





If a pair of integers have different signs, then the answer will
be negative. You must calculate the absolute value of each
integer and then divide the first integer by the second
integer.


Example 1: -2 · (-5) = 10
Example 2: 2 · 5 = 10







When multiplying two integers having the same sign, the
product is always positive


Example: -10 / -2 = ?




answer is
Step 1: group the first two numbers and use rules I and II
above to calculate the intermediate step
(-1) · (-2) = +2 (used rule I)


Step 2: use result from intermediate step 1 and multiply by
the third number.



2 · (-3) = -6 (used rule II)
5
6
Subtracting Integers
• Convert the problem to addition.
Ex. 12-(-36) to 12+36. remember
to change the last number of the
sequence from negative to
positive or positive negative.
• Add or subtract the problem like
a regular math problem. Ex.
12+36=48.
• Ex
126-(-176)
126+176=302 or
126-176
126+(-176)=(-50) or
-126-(-176)
-126+176=50
(note)
when you add integers remember
that when you add integers with
the same sign the answer is going
to be the same as the sign, but if
the absolute value of the negative
number is higher than the
positive than the numbers going
to be a negative.
7
When the number in the equation is negative
positive you
thenadd
the opposite
you
convert the
to the
number
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to aThen
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you Then
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you
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change
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thisadd
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thethe
variable
opposite
is
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alone
onisthe
onone
the side
other.
of the equal sign, and the
difference of the answer and the opposite number
is on the other.
Example
X-(-13)=13
X+13=26
X+13+(-13)=26+(-13)
X+13+(-13)=26+(-13)
26+(-13)=13
26+(-13)=13
13+(-13)=0
13+(-13)=0
X=13
X=13
13-(-13)=26
13+13=26
8
9
Distributive Property For Algebra
Take both numbers in the parentheses and
multiply them separately to the number outside
of the parentheses, still using the sign in
between both numbers in parentheses.
Ex. 1 :
turns into
Ex. 2 : 5(-Y+9) turns into 5(-Y)+59 = 5(- Y)+45
Ex. 3: -5(Y-9) turns into -5Y-(-59) = -5Y - (-45)
How to Solve Equations
Step 1
Created
Step 2 By:
Step 3
Jonah
A legal move (you have to do the
same thing to both sides) is very
simple.
What you are trying to do here is; you want to get the variable alone. All you have to
Once
thethe
constant
is gone,
add the same number you added to the sum,
do
is add
opposite
to theyou
constant
then whatever you get from that equation, is what the variable equals
Example:
X + 5 = 12
Example:
X + 5 + (-5) = 12 + (-5)
X + 5 + (-5) = 12 + (-5)
X = 7
10
By: Cameron
When subtracting integers you “add the opposite”.
Example: 12-8=4
12+(-8)=4
 Rule
When Subtracting Integers you add the opposite.
Example: 10-(-4)=14
10+4=14
Do you want to know how this works~ click to find
11
out.
Just draw a number line if it helps you more.
Also when you have a subtraction sign next to a parenthesis.
You change the sign to addition and the negative number to
a positive.
Example: -10-(-4)=14
10+4=14
Example2: -10-(4)=6
-10+-4=14
12
HOW TO COMBINE LIKE TERMS
Congrats
you can nowALGEBRAIC
simplify algebraic
A.K.A. SIMPLIFYING
EXPRESSIONS
expressions!!!!!!!!
 Terms --- The
Step 13 Hint
The only like terms are
3x & 2x

begin
with an
You
Begin
simplifying
simplify
Step 2
 Before
Algebraic Expression to
3x+y+2x+7=?
3x+2x=5x
Final answer
and find…………………..
5x+y+7
The Surprise
Expression
we simplify, find the terms, like
terms, coefficients, and constants.
algebraic expression
separated between each
plus or minus sign
Ex. 3x, y, 2x, 7
 Like terms --- Terms
that conduct the same
variables
Ex. 3x & 2x
 Coefficients --- The
numbers that are
involved with a variable
Ex. 3, 2, 1
 Constants --- Terms
without an variable
Ex. 7
By Lennon Dresnin
You solve an algebraic equation by doing different sets of
legal moves. You do a legal move by adding or subtracting and
in some cases multiplication and dividing what you do to one
side to the other until you cant do anymore moves.
example: 3+4+-4=Y+4+-4+3